What is the cardinality of a graph?

What is the cardinality of a graph?

The order of a graph G is the cardinality of its vertex set, and the size of a graph is the cardinality of its edge set. Given two vertices u and v, if uv ∈ E, then u and v are said to be adjacent. In this case, u and v are said to be the end vertices of the edge uv.

What is the diameter of a graph?

is a graph distance. In other words, a graph’s diameter is the largest number of vertices which must be traversed in order to travel from one vertex to another when paths which backtrack, detour, or loop are excluded from consideration.

What does the degree of a vertex represent in the acquaintanceship graph?

Degree of a vertex u= Number of acquaintances of u Neighborhood of a vertex u= All acquaintances of u Isolated vertices = All people with no acquaintances Pendant vertices = All people with exactly 1 acquaintance Average degree = On average, people have 1000 acquaintances.

What is a tie in a graph?

In undirected graphs, the ties have no direction. For example, in Figure 1 above, there is a relationship between a and b, and this is the same thing as saying there is a relationship between b and a. In directed graphs (also known as digraphs), the ties do have direction.

What is cardinality of graph in graph theory?

The number of vertices, the cardinality of V, is called the order of graph and denoted by |V|. We usually use n to denote the order of G. The number of edges, the cardinality of E, is called the size of graph and denoted by |E|. We usually use m to denote the size of G.

How do you find the cardinality of a function?

The cardinality of a finite set A (denoted |A|) is the number of elements in set A. i ∈ {1, 2, . . . k}. For finite sets A, B, if there is a surjective function f : A → B then |B|≤|A|, and if there is a bijective function f : A → B then |A| = |B|.

What does the degree of vertex represent?

In graph theory , the degree of a vertex is the number of edges connecting it. A vertex with degree 1 is called an “end vertex” (you can see why). …

What is the vertex of the graph What does the vertex represent?

Vertex. If the parabola opens up, the vertex represents the lowest point on the graph, or the minimum value of the quadratic function. If the parabola opens down, the vertex represents the highest point on the graph, or the maximum value. In either case, the vertex is a turning point on the graph.

What is strong tie in graph?

STRONG AND WEAK TIES. strong ties than when they are weak ties. This suggests the following qualitative assumption: If a node A has edges to nodes B and C, then the B-C edge is especially likely to form if A’s edges to B and C are both strong ties.

What represent relationship as nodes and ties?

A graph (sometimes called a sociogram) is composed of nodes (or actors or points) connected by edges (or relations or ties).